Photochemical synthesis of dendritic silver particles

ABSTRACT

Forming dendritic silver particles by combining silver ions, a reducing agent, and a polymer comprising amine groups in an aqueous solution to yield a precursor solution, and irradiating the precursor solution with ultraviolet radiation to form a multiplicity of dendritic silver particles. A desired morphology of the dendritic particles, including branch and junction density, may be achieved by selecting growth parameters, such as molar ratio of amine groups to silver ions, a length of time of irradiating, or both.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Patent Application No.62/750,615 entitled “PHOTOCHEMICAL SYNTHESIS OF DENDRITIC SILVERPARTICLES” and filed on Oct. 25, 2018, which is incorporated herein byreference in its entirety.

TECHNICAL FIELD

This invention relates to photochemical synthesis of dendritic silverparticles.

BACKGROUND

Over the last several years, the global value of counterfeit goods hasexceeded half a trillion dollars. In addition to direct economic lossesto manufacturers, counterfeit materials, parts and assemblies typicallyprovide inferior performance and poor reliability, which can causesecurity issues, such as security risks for national defense. There isan increasing demand for high trust, high reliability taggingmethodologies, in which genuine articles manufactured in a legitimatefacility carry “trust elements” incapable of being cloned. Currentphysical tagging technologies include holograms, coded tags, DNAsignatures, mechanical deformation, and fabricated nanostructures.However, such techniques have several disadvantages, includingdifficulties in manufacture, lack of structural stability andreliability, and complicated readout procedures.

Fractal structures, such as synthetic dendritic silver particles, arepromising candidates for physical identifiers to combat counterfeiting.For example, dendritic silver particles can be applied to an item anddecoded to yield a large exclusive integer, which can be mapped to theitem in a secure database. Traditionally, dendritic silver particles areprepared using organic reducing agents, ultrasonically assistedtemplated synthesis, direct replacement reactions, photoreduction,plating, γ-irradiation, magnetic field assisted growth, or pulsedsonoelectro-chemical methods. These methods, however, typically requirea long preparation time and/or precisely controlled environmentalconditions that are not conducive to mass manufacturing. In addition,the morphology of dendritic silver particles obtained by these methodscan lack natural diversity.

SUMMARY

Dendritic silver particles are synthesized by a photochemical process ofirradiating an aqueous precursor solution containing silver ions, aconjugate base of a weak acid, and a polymer comprising amine groups.This process yields dendritic silver particles after 20 minutes or lessof UV irradiation under ambient conditions. The size and shape of theparticles can be altered by varying experimental parameters, such aslength of irradiation and local chemical environment. Unique dendriticstructures obtained by this process have distinctive morphologicalcharacteristics suitable for tagging and securing manufactured items.The dendritic silver particles synthesized by this process can reachsizes of up to about 100 which allows structural information about theparticles to be quickly read and analyzed by optical microscopy, therebyfacilitating the use of the particles as anti-counterfeiting labels insupply chains.

In a general aspect, dendritic silver particles are formed by combiningsilver ions, a reducing agent, and a polymer comprising amine groups inan aqueous solution to yield a precursor solution, and irradiating theprecursor solution with ultraviolet radiation to form a multiplicity ofdendritic silver particles.

Implementations may include one or more of the following features.

The reducing agent may include an organic acid (e.g., citric acid orascorbic acid). A molar ratio of silver ions to the conjugate base ofthe weak acid in the precursor solution is typically in a range of about3 to about 3.5. In one example, the polymer is poly(allylamine). A pH ofthe precursor solution is in a range of about 12 to about 13. A molarratio of amine groups to silver in the precursor solution is betweenabout 6 and about 12. Irradiating the precursor solution occurs underambient conditions. The precursor solution is typically irradiated withultraviolet radiation for at least 3 minutes, up to 20 minutes, or both.The wavelength of the ultraviolet radiation is typically in a range ofabout 320 nm to about 400 nm. The ultraviolet radiation has an outputpower in a range of about 1.5 W/cm² to about 4 W/cm².

The dendritic silver particles typically have a linear dimension up toabout 100 microns. In some cases, the dendritic silver particles aredendritic silver nanoparticles. The dendritic silver particles compriseat least 95 wt % silver. A branch density of the dendritic silverparticles is in a range of about 0.1×10⁵ branch/mm² to about 11×10⁵branch/mm². A junction density of the dendritic silver particles is in arange of about 1×10⁴ junction/mm² to about 36×10⁴ junction/mm². Afractal dimension of the dendritic silver particles is in a range ofabout 1.4 to about 1.9. Each dendritic silver particle of themultiplicity has a unique structure. In some cases, selecting a molarratio of amine groups to silver, a length of time of the irradiating, orboth is selected to achieve a desired morphology of the multiplicity ofdendritic silver particles.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an exemplary scheme for synthesis of dendritic silverparticles.

FIGS. 2A-2B show samples of precursor solution before and after thesolution is subjected to UV irradiation, respectively.

FIGS. 3A-3C show electron microscopy images of the structure ofdendritic silver particles.

FIG. 4 shows the energy-dispersive X-ray spectrometry spectrum for anexemplary branch of a dendritic silver particle.

FIGS. 5A-5C show transmission electron microscopy images of dendriticsilver particles at 30 seconds, 60 seconds, and 3 minutes of ultraviolet(UV) irradiation, respectively.

FIG. 6A depicts the growth mechanism of dendritic silver particles. FIG.6B depicts a proposed structure of a silver particle-poly(allylamine)((AgNP)-PAAm) complex that enables the formation of dendritic particles.

FIG. 7 shows dendritic silver particles synthesized from precursorsolutions containing various amine/silver ratios. The scale barsrepresent 500 nm.

FIGS. 8A-8E show patterns of dendritic silver particles formed after 20minutes of UV irradiation.

FIG. 9 depicts an exemplary skeleton analysis for identification ofdendritic branch levels.

FIGS. 10A-10E show branch length distribution plots for five types ofdendritic silver particle patterns.

FIG. 11 shows a plot of dendritic silver particle branch densities as afunction of fractal dimension.

FIG. 12 shows molecular structures of silver particles during thesynthesis of dendritic silver particles using a precursor solutioncontaining allylamine (AAm).

FIG. 13 depicts molecular structural changes that occur during synthesisof dendritic silver particles.

FIG. 14 shows a plot of the average branch length of dendritic silverparticles as a function of the amine/silver ratio of the precursorsolution.

FIGS. 15A-15E show distributions of the weighted number of branches of aspecific length (w) as a function of branch length (L) for five types ofdendritic silver particle patterns.

DETAILED DESCRIPTION

A method for synthesizing dendritic silver particles is described. Thismethod includes steps of combining silver ions, a reducing agent, and apolymer comprising amine groups in an aqueous solution to yield aprecursor solution, and irradiating the precursor solution withultraviolet radiation to form a multiplicity of dendritic silverparticles. Examples of suitable reducing agents for the precursorsolution include organic acids, such as citric acid and ascorbic acid.An example of a suitable polymer comprising amine groups in theprecursor solution is poly(allylamine) (PAAm). The pH of the precursorsolution is typically in a range of about 12 to about 13. The molarratio of silver ions to weak acid in the precursor solution is typicallyin a range of about 3 to about 3.5. The molar ratio of amine groups tosilver in the precursor solution is typically in a range of about 6 toabout 12. The described method of synthesizing dendritic silverparticles may be conducted under ambient conditions. As used herein,“ambient conditions” generally refers to a combination of common orprevailing temperature, pressure, and relative humidity found in alaboratory or manufacturing setting.

Irradiation of the precursor solution to synthesize dendritic silverparticles is performed using ultraviolet (UV) radiation. The precursorsolution may be irradiated for a length of time between about 3 minutesand about 20 minutes or more to achieve a desired variation in the sizeand patterns of the dendritic silver particles. A wavelength of the UVradiation is typically from about 320 nm to about 400 nm (e.g., UVA),and the output power of the UV radiation is in typically in a range ofabout 1.5 W/cm² to about 4 W/cm².

The dendritic silver particles synthesized by the described method havedefined geometric features, including a core and dendritic branches thatextend from the core. The dendritic silver particles also includejunctions (or nodes) at which the dendritic branches meet. Thesegeometric features, or minutiae, of the dendritic silver particlescreate unique patterns and structures that enable individual particlesto be identified out of the multiplicity of particles. The branchdensity of the dendritic silver particles synthesized by the describedmethod ranges from about 0.23×10⁵ branch/mm² to about 10.4×10⁵branch/mm². The junction density of the dendritic silver particlessynthesized by the described method ranges from about 1.0×10⁴junction/mm² to about 35.8×10⁴ junction/mm². Individual particles may bedistinguished from the multiplicity of particles by determining thefractal dimension of the particle. The fractal dimension of thedendritic silver particles synthesized by the described method rangesfrom about 1.4 to about 1.8.

The dendritic silver particles synthesized by the described method canhave a size of up to about 100 microns. As used herein, “particle size”refers to the linear dimension from the end of one dendrite (i.e.,branch) of the particle to the end of an opposing dendrite of theparticle. In some implementations, the dendritic silver particlescreated by the described method are nanoparticles. As used herein,“nanoparticle” refers to particles with a dimension in a range of about20 nm to about 1000 nm. The dendritic silver particles created by thedescribed process are substantially pure silver (e.g., at least 95 wt %silver).

FIG. 1 depicts an exemplary setup 100 for synthesis of dendritic silverparticles using a process of polymer-assisted photolysis. A precursorsolution 102 for synthesis of dendritic silver particles may be obtainedby combining silver nitrate, sodium citrate, and a poly(allylamine)(PAAm) solution. In one example, a precursor solution was prepared bycombining silver nitrate and sodium citrate at a 2:1 molar ratio with apoly(allylamine) (PAAm) solution containing a ˜1 M amine group. Aphoto-reduction of nitrate and a polymeric ligand was selected for theprecursor solution to achieve synthesis of dendritic silver particlesunder ambient conditions. The precursor solution was exposed to UVradiation. In one example, the precursor solution was irradiated by a365 nm UV light for 3 minutes. As a result of UV radiation, smalldendritic silver particles were formed. A change in color of theprecursor solution 200 and 202 in FIGS. 2A and 2B, respectively, wasobserved as a result of the UV radiation, indicating the presence ofdendritic silver particles. The dendritic silver particles bound to thePAAm and served as seeds for further growth. The bounded particlesconnected via crystal growth under the presence of citrate and freeamine groups. Following irradiation, polymeric ligands formed a polymerbackbone to create a chain tethering together the particles. Some aminegroups fixed the relative positions of dendritic silver particles byforming N—Ag coordination bonds. Free amine groups served as a reducingagent that facilitated Ag growth, especially inter-particle growth.

As shown in FIGS. 3A and 3B, presence of dendritic silver particles 300was confirmed using transmission electron microscopy (TEM). Thedendritic silver particles 300 contained a dense core 302 and extendedbranches 304. Each branch was composed of silver particles approximately50 nm in size. The composition of the dendritic silver particles 300 wasfurther analyzed using scanning electron microscope (SEM) (as shown inFIG. 3C). As shown in FIG. 4, energy-dispersive X-ray spectrometry ofthe particles revealed a high abundance of Ag (39.14%), indicating thatthe particles obtained from the precursor solution were substantiallypure silver. The remaining elements are believed to be from thesubstrate (e.g., carbon coated copper TEM grid). Silver distributionmatched the morphology of the observed dendritic particles.

As shown in FIGS. 5A and 5B, as radiation time increased to 60 seconds,a densely packed Ag core 500 emerged, with newly formed particles 502extending from the edges. As shown in FIG. 5C, further increasing the UVexposure time to 3 min resulted in the formation of dendritic particles504. As indicated by FIGS. 5A-5C and 6A, the formation of dendrites,rather than simple isotropic growth, is preferred due to the localchemical gradient created by PAAm. The chemical concentration gradientaround the growth front of crystals is vital in the formation ofdendritic particles. As shown in FIG. 6A, the presence of PAAm providesa nanoscale chemical gradient for formation of dendritic silverparticles. Fixation of a portion of the silver particles by PAAm createsa steric effect that results in the fixed silver particles havingimproved accessibility to reagents compared to non-fixed silverparticles, creating a first chemical gradient. In addition, thedistribution of free amine groups on PAAm is anisotropic with regard toindividual silver particles, resulting in a second degree of chemicalgradient.

The dendritic AgNPs are believed to grow in a two-step process. First,during nucleation, small AgNPs form after UV illumination through thephotoreduction of silver nitrate with sodium citrate as the reducingagent, and further bind PAAm to yield clusters. Next, during growth, theclusters serve as seeds to guide the further growth of Ag crystals underthe presence of reducing agents (e.g., citrate and PAAm). FIG. 6Bdepicts a proposed structure of a silver particle (AgNP)-PAAm complex600 that enables the formation of dendritic particles. The amine groupbetween AgNPs 602 indicated by dashed curves 604 facilitates theanisotropic growth of silver.

Alteration of the local chemical environment changes the relativereaction rate of Ag nucleation and seeded growth, which results insignificant changes in the morphology of the silver particles. Theamine/Ag⁺ ratio (N/Ag) can be adjusted to alter the local chemicalenvironment. In one example, precursor solutions with N/Ag ratios of 1,2, 4, 6, 10, 12, and 20 were tested and the corresponding productsobtained after 3 minutes of UV irradiation were analyzed. As shown inFIG. 7, five distinctive dendritic morphologies 700, 702, 704, 706, and708 were observed. For precursor solutions with N/Ag<6, only randomsilver particle aggregates formed as a result of insufficient aminegroups. Dendritic silver particles possessing long major branches andshort sub-branches started to form at N/Ag ratios equal to 6. Someindividual silver particles that did not have a chance to grow can beobserved. For precursor solutions with N/Ag ratios equal to 6-8 (700 and702), the sub-branches were longer, and a well-branched dendriticstructure was observed. Further increasing the N/Ag ratio to 8-10 (704and 706) led to the formation of medium and long sub-branches, and theapparent number of branches started to reduce. When the N/Ag ratio ofthe precursor solution was equal to 10 (706), a further reduction inbranch number was observed and the as-formed dendritic structuresfeatured very long branches and sub-branches. Increasing the N/Ag ratioto 12 (708) led to formation of small particles with very thickbranches. Only individual silver particles were observed when the N/Agratio of the precursor was above 12.

The size of dendritic particles can be adjusted by increasing ordecreasing the irradiation time. In one example, the irradiation timewas increased to 20 minutes. As shown in FIGS. 8A-8E, the size of the Agparticles (type I-type V, or 800, 802, 804, 806, and 808, respectively)increased by approximately 1-2 orders of magnitude when the irradiationtime was increased from 3 minutes to about 20 minutes. Dendriticpatterns as large as 50-100 μm can be formed by adjusting irradiationtimes to about 20 minutes.

Mathematical analysis of the dendritic Ag patterns may be performed toreveal their unique structures, as well as their potential asinformation carriers. The type and position of minutiae, geometricfeatures of the particles, confer uniqueness on a dendritic pattern anddistinguish one pattern from all others. For dendritic silver particles,the junctions (or nodes) of the dendrites are the relevant minutiae. Ameasurable parameter in each of the nodes may be used to represent avalue of modulus B such that the total number of possible patterns isgiven by B^(no), where n_(o) is the number of junctions measured. Forexample, if the position of each junction was read as being in either aneven (0) or odd (1) numbered location in a Cartesian grid overlay, thenB=2. When the junction density is 10⁵ per mm² and the reading resolutionis 3 μm, the total number of possible patterns in a 50 μm×50 μm dendritearea is in the order of 10⁷⁵, which is more than enough to tag everymanufactured item. Considering the junction density and the branchlength distributions shown in Table 1 below, type III patterns may bemost suitable for tagging purposes as they possesses a high junctiondensity and a greater portion of branches over 3 μm in length.

TABLE 1 Exemplary branch and junction densities for five pattern typesof dendritic silver particles Pattern type I II III IV V Branches per2.7 ± 3.9 ± 2.0 ± 0.35 ± 8.0 ± mm² 0.50 × 0.09 × 0.78 × 0.12 × 2.4 × 10⁵10⁵ 10⁵ 10⁵ 10⁵ Junctions per 9.7 ± 15.7 ± 8.1 ± 1.5 ± 26.2 ± mm² 2.9 ×0.5 × 3.6 × 0.5 × 9.6 × 10⁴ 10⁴ 10⁴ 10⁴ 10⁴

In one example, image analysis was performed using ImageJ. Skeletonanalysis of a dendrite may be conducted to reveal branch and junctioninformation, such as first, second, and third branches 900 and junctions902 depicted in FIG. 9. FIGS. 10A-10E show changes in the N/Ag ratio ofthe precursor solution resulted in variations in branch/junctiondensities and distinctive branch length distributions. As shown in Table1, when N/Ag ratio of the precursor solution increased, thebranch/junction density also increased (type II), and then dropped untilthe N/Ag ratio of the precursor solution reached 10. Type V patternspossessed the highest branch/junction density. This trend was verifiedusing optical imaging (FIGS. 8A-8E). When the N/Ag ratio of theprecursor solution was relatively low, increasing the N/Ag ratioresulted in increased branching. As N/Ag ratio of the precursor solutionfurther increased, longer but fewer branches were favored. At very highN/Ag ratios, small and highly dense branches were formed.

As shown in Table 2, essentially all of the dendritic silver particlepatterns were found to be perfect dendritic structures and weredistinguishable according to their fractal dimension (FD). As shown inFIG. 11, formation of fractal structure is driven by reaction dynamics.Branch density increased as a power of FD.

TABLE 2 Exemplary fractal dimension of five pattern types of dendriticsilver particles Pattern type I II III IV V FD 1.716 ± 1.671 ± 1.571 ±1.41 ± 1.821 ± 0.013 0.017 0.046 0.058 0.015 R² 0.998 0.999 0.999 0.9980.999

EXAMPLE

Silver nitrate (ACS reagent, ≥99.0%), sodium citrate dehydrate (≥99.0%),allylamine (≥99.0%) and poly(allylamine) solution (Mw˜17,000, 20 wt. %in H2O) were purchased from Sigma-Aldrich. 400 mesh ultra-thin carboncoated TEM grids were purchased from Ted Pella.

Dendritic silver particles were synthesized via polymer-assistedphotolysis. A precursor solution for silver particle synthesis wasobtained by first combining 204 mg silver nitrate and 134 mg sodiumcitrate dehydrate in 200 mL DI water. A poly(allylamine) (PAAm) solutioncontaining ˜1 M amine group was obtained by diluting 20% PAAm solution.1 mL of the silver nitrate/sodium citrate solution was mixed with thePAAm solution, with the final precursor solution having an equivalentmolar ratio of amine group and Ag⁺ ions (N/Ag) of 10:1. For samples withdifferent N/Ag values, the amount of PAAm solution added was adjustedaccordingly to mix with 1 mL silver nitrate/sodium citrate solution toachieve a final precursor solution having an equivalent molar ratio ofamine group and Ag⁺ ions (N/Ag) of 10:1. For the purpose of comparison,the synthetic process was also repeated by replacing PAAm withallylamine (AAm).

The final precursor solution was subjected to UV radiation. UV radiationwas applied using a BlueWave® 200 UV curing spot lamp. The output powerof the UVA band was adjusted to 3.0 W/cm². The wavelength of the UVradiation was about 365 nm.

The reaction products were deposited on a TEM grid following irradiationfor TEM and SEM analysis. TEM images were captured using a Philips CM 12TEM. SEM and energy-dispersive X-ray spectrometry (EDX) data wasobtained using a Hitachi S4700 FESEM.

Microscopic images of the reaction products were obtained using anOlympus BX53 microscope. For optical imaging, reaction products weredrop-casted onto a glass slide cleaned with Harrick plasma cleaner. Thereaction products were allowed to dry in air overnight before imaging.

As shown in FIG. 12, for mixtures containing AAm, rather than PAAm, asthe ligand and reducing agent, no dendritic particles were formed. Inmixtures containing AAm, silver particles 1200 were bound to the smallmolecule ligands and remained subject to random movement in the aqueoussolution. As a result, particles could not be connected efficientlythrough crystal growth. By comparison, in mixtures containing PAAm, thepolymeric ligand was able to fix the relative positions of adjacentsilver particles, so that inter-particle Ag growth could occur. Asdepicted in FIG. 13, the relative position of the initially formedsilver particles 1300 was fixed by PAAm chains 1302 through chelation,which resulted in variation of the accessibility of individual silverparticles to citrate ions 1304. For example, silver particles 1300located at the edge of polymer chains 1302 had a greater chance tocontinue growing under the presence of a reducing agent. In addition,the local distribution of free amine groups varied for individual silverparticles 1300, leading to an anisotropic growth of Ag under continuousUV irradiation.

Optical images of dendritic silver patterns were analyzed using ImageJ(Fiji version). Fractal box analysis was conducted by converting imagesto 8 bit and using the “fractal box count” function. The box size waschosen to be 2, 3, 4, 6, 8, 12, 16, 32 and 64. The number of boxescontaining a fraction of the image was counted. All of the patternsobserved were perfect dendritic structures, demonstrated by the high Rvalues in linear regression shown in Table 2. The FD value for variouspattern types varied from 1.41 to 1.82 (Table 2). The standard deviationof FD for a specific type of pattern was much smaller than thedifference in FD between the various pattern types, making it possibleto readily distinguish pattern types according to FD.

In order to count the number of branches and junctions of the dendriticsilver particles, the 8 bit image was first skeletonized and thenanalyzed using the “analyze skeleton” function. The skeletonizationfunction classified the distance between two adjacent junctions (or onejunction and one end) as a branch. The junction/end was defined as avoxel that had more than two neighbors or only one neighbor,respectively. The shortest branch method was used to prune the ends toeliminate loops and end-points. For accuracy, at least three images wereanalyzed for each type of pattern.

As shown in FIG. 9, different levels of branches may be observed indendritic patterns corresponding to the order of silver growth, with thesmallest n^(th) level branch the result of Ag particles that attached tothe Ag nanowire network. The number of branches increased as the orderof silver growth increased. Branch density increased following anear-exponential trend as the FD increased, as shown in FIG. 11. This isexplained by the fact that FD is a measurement of surface coverage andfollows a scaling rule:

N=ϵ ^(−FD)

where the variable N stands for the number of segments, and ε is thescaling factor. The only deviation from the scaling rule observed was intype I patterns, which may be the result of increased branch thicknesscompared to the other pattern types.

Changes in the N/Ag ratio resulted in an alteration in the reactionrate, which lead to variations in branch/junction densities anddistinctive branch length distributions (FIGS. 10A-10E). For type I andtype II patterns, the branch length distribution was fitted by a singleGaussian function with peak centers located at 1.3 μm and 1.5 μm,respectively. Compared with type I patterns, the branches in the type IIpattern had a narrower distribution. Additional Gaussian peaks wereobserved in type III patterns at 4.2 μm and type IV patterns at 5.4 μm,which corresponds to longer branches and indicates that the growth speedof the Ag crystals exceeded the seeding speed under those conditions.The longest branches only exist as first level branches due to stericeffects (FIG. 9). As a result, the major portion of branches stillfeatured a shorter length. The average branch length dropped to 0.8 μmfor type V patterns. The drop in branch length may be due to theinsufficiency of free silver ions, as most silver ions were chelated bythe amine groups on PAAm, which hindered crystal growth.

As shown in FIG. 14, the average branch length (L) generally reflectedthe same findings. To analyze the branching characters in dendritic Agpatterns, a parameter w was defined as the weighted number of branchesat a specific length. The value of w represents the total length of Agthat grows into a specific type of branch. By definition, w=N_(L)×L,where N_(L) is the number of branches with length L. Each type ofdendritic pattern can be distinguished by the distribution of w as afunction of branch length (FIGS. 15A-15E). In the w-L plot, severallinear trends can be observed for each type of dendritic structure. Theslope of the linear trends represents NL, and for each linear trend NLis the same. In addition, the linear trend with the lower slopetypically possesses a greater average length. Each linear trendrepresents one level of branching. The trend with the smallest slopecomes from level 1 branching, which is the major branch that first formsin the solution. Similarly, the trend with the second, third, . . . ,m^(th) smallest slope will be level 2, 3, . . . , m branches. The numberof distinguishable linear trends indicates the number of times thestructure has copied itself. For type II, III and IV patterns, fourlevels of branches are identified, demonstrating a significantcomplexity for these pattern types. For type I and V, three levels areobserved, indicating a lower complexity for these pattern types.

Application. Two tags were made using the dendrites, and a series oftests were performed to verify if it is possible to discriminatefeatures from different tags. Two rectangular regions of 90 μm×50 μmwere located under the microscope, and denoted as tag I and tag II. Themicroscopic features of them were recorded to establish a database. TagI was assumed to be the label of an authentic or wanted object, whiletag II was a control. Five square regions 25 μm×25 μm were randomlychosen from tag I and tag II, which were set as keys to be identified. Ascale-invariant feature transform (SIFT) analysis was performed toidentify those keys via comparing feature points. It was found that allthe keys selected from tag I could be readily identified. Tens tohundreds of matching feature points were found between tag I and key1-4, the positions of which accurately matched the regions that the keyswere selected from. On the other hand, key 5 selected from tag II didn'tshow any match to tag I, although both tags were generated from the samebatch of Ag dendrites. The results showed that the dendritic featurespossessed great ability to form unique taggants. Moreover, theinformation contained in a tiny region was already sufficient foridentification, which has several advantages. First, the cost for asingle tag could be readily reduced. For example, tags with a dimensionof 100 μm×100 μm would be sufficiently large for encryption, which onlycost 2 nL of the Ag dendrite suspension. Second, it is possible toproduce a vast number of tags from a single batch of product (5×10⁵ tagsper mL). Third, a tag could still be accurately identified even if mostof it were damaged, which makes the tag highly durable and reliable.

In summary, a photochemical method to synthesize various types ofdendritic AgNPs has been demonstrated. Experimental parameters (e.g.,N/Ag ratio and illumination time) were found to affect the morphologiesof the dendrite AgNPs. Moreover, the size and morphology of thoseparticles can be uniquely generated and readily tuned by choosingappropriate growth parameters (e.g., N/Ag and illumination time).Optical imaging and mathematical analysis revealed that dendriticparticles grown under the different conditions could be welldistinguished based on their branch/junction densities and branchlengths. Further, the superior ability of the as-prepared dendrites toproduce vast numbers of unique patterns makes it perfectly suitable forphysical tagging for anti-counterfeiting and security purposes.

A number of embodiments have been described. Nevertheless, it will beunderstood that various modifications may be made without departing fromthe spirit and scope of the disclosure. Accordingly, other embodimentsare within the scope of the following claims.

What is claimed is:
 1. A method of forming dendritic silver particles,the method comprising: combining silver ions, a reducing agent, and apolymer comprising amine groups in an aqueous solution to yield aprecursor solution; and irradiating the precursor solution withultraviolet radiation to form a multiplicity of dendritic silverparticles.
 2. The method of claim 1, wherein the reducing agentcomprises an organic acid.
 3. The method of claim 1, wherein thereducing agent comprises citric acid or ascorbic acid.
 4. The method ofclaim 1, wherein a molar ratio of silver ions to the conjugate base ofthe weak acid in the precursor solution is in a range of about 3 toabout 3.5.
 5. The method of claim 1, wherein the polymer comprisingamine groups is poly(allylamine).
 6. The method of claim 1, wherein a pHof the precursor solution is in a range of about 12 to about
 13. 7. Themethod of claim 1, wherein a molar ratio of amine groups to silver inthe precursor solution is between about 6 and about
 12. 8. The method ofclaim 1, wherein irradiating the precursor solution occurs under ambientconditions.
 9. The method of claim 1, wherein the precursor solution isirradiated with ultraviolet radiation for at least 3 minutes.
 10. Themethod of claim 9, wherein the precursor solution is irradiated withultraviolet radiation for up to 20 minutes.
 11. The method of claim 1,wherein the wavelength of the ultraviolet radiation is in a range ofabout 320 nm to about 400 nm.
 12. The method of claim 1, wherein theultraviolet radiation has an output power in a range of about 1.5 W/cm²to about 4 W/cm².
 13. The method of claim 1, wherein the dendriticsilver particles have a linear dimension up to about 100 microns. 14.The method of claim 1, wherein the dendritic silver particles aredendritic silver nanoparticles.
 15. The method of claim 1, wherein thedendritic silver particles comprise at least 95 wt % silver.
 16. Themethod of claim 1, wherein a branch density of the dendritic silverparticles is in a range of about 0.1×10⁵ branch/mm² to about 11×10⁵branch/mm².
 17. The method of claim 1, wherein a junction density of thedendritic silver particles is in a range of about 1×10⁴ junction/mm² toabout 36×10⁴ junction/mm².
 18. The method of claim 1, wherein a fractaldimension of the dendritic silver particles is in a range of about 1.4to about 1.9.
 19. The method of claim 1, wherein each dendritic silverparticle of the multiplicity has a unique structure.
 20. The method ofclaim 1, further comprising selecting a molar ratio of amine groups tosilver, a length of time of the irradiating, or both to achieve adesired morphology of the multiplicity of dendritic silver particles.